code: def test_predict_interaction(daily_data):
      """Tests interaction between predict date and parameter `d`.
      Arima can not predict below `d`."""
      model = AutoArimaEstimator(d=10)
      df = daily_data["df"]
      train_df = daily_data["train_df"]
      test_df = daily_data["test_df"]
      model.fit(train_df, time_col=TIME_COL, value_col=VALUE_COL)
  
      # predict start date < d
      # Predicted, lower and upper CI values of the first 4 (10-6) days should be NaN
      predicted = model.predict(df[6:])
      print(predicted.head(10))
      assert (
          (
              predicted[
                  [
                      PREDICTED_COL,
                      PREDICTED_LOWER_COL,
                      PREDICTED_UPPER_COL,
                  ]
              ][0:4]
          )
          .isnull()
          .values.all()
      )
      assert (
          not (
              predicted[
                  [
                      PREDICTED_COL,
                      PREDICTED_LOWER_COL,
                      PREDICTED_UPPER_COL,
                  ]
              ][5:10]
          )
          .isnull()
          .values.any()
      )
  
      # predict start date > d
      # Predicted, lower and upper CI values should not be NaN
      predicted = model.predict(df[12:])
      assert (
          not (
              predicted[
                  [
                      PREDICTED_COL,
                      PREDICTED_LOWER_COL,
                      PREDICTED_UPPER_COL,
                  ]
              ][0:4]
          )
          .isnull()
          .values.any()
      )
  
      # predict start date > train end date
      # Predicted, lower and upper CI values should not be NaN
      predicted = model.predict(test_df[5:])
      assert (
          not (
              predicted[
                  [
                      PREDICTED_COL,
                      PREDICTED_LOWER_COL,
                      PREDICTED_UPPER_COL,
                  ]
              ][0:4]
          )
          .isnull()
          .values.any()
      )
  
imports: import numpy
  import pandas
  import pytest
  from pmdarima.arima import AutoARIMA
  from sklearn.metrics import mean_absolute_error
  from sklearn.metrics import mean_squared_error
  from testfixtures import LogCapture
  from greykite.common.constants import LOGGER_NAME
  from greykite.common.constants import PREDICTED_COL
  from greykite.common.constants import PREDICTED_LOWER_COL
  from greykite.common.constants import PREDICTED_UPPER_COL
  from greykite.common.constants import TIME_COL
  from greykite.common.constants import VALUE_COL
  from greykite.common.evaluation import EvaluationMetricEnum
  from greykite.common.evaluation import calc_pred_err
  from greykite.common.logging import LoggingLevelEnum
  from greykite.common.python_utils import assert_equal
  from greykite.common.testing_utils import generate_df_for_tests
  from greykite.sklearn.estimator.auto_arima_estimator import AutoArimaEstimator
label_desc: Use image node_id 10 for calling a global function with example usage: test_predict_interaction(daily_data) without return types